Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. Benzenoid Hydrocarbons

1999 ◽  
Vol 39 (2) ◽  
pp. 289-293 ◽  
Author(s):  
Svetlana Marković ◽  
Ivan Gutman
Keyword(s):  
Adjacency Matrix ◽  
Benzenoid Hydrocarbons ◽  
Spectral Moments ◽  
Molecular Graphs

Topological Properties of Circumcoronenes

1998 ◽  
Vol 53 (8) ◽  
pp. 699-703 ◽  
Author(s):  
Ivan Gutman ◽  
Sven J. Cyvina ◽  
Vesna Ivanov-Petrović
Keyword(s):  
Regular Hexagon ◽  
Topological Properties ◽  
Benzenoid Hydrocarbons ◽  
Spectral Moments ◽  
Energy Effect ◽  
Cyclic Conjugation ◽  
Clar Structures ◽  
First Time ◽  
Structural Invariants

Abstract The regular-hexagon-shaped benzenoid hydrocarbons: B1 = benzene (C6H6), B2 = coronene (C24H12), B3 = circumcoronene (C54H18), B4 = circumcircumcoronene (C150H30), etc. possess unique topological properties. General expressions for the most important of such properties (number of fun-damental structural invariants, number of Kekule and Clar structures, number of aromatic sextets, Wiener and Szeged indices, spectral moments) are given, including a number of results that are communicated here for the first time. Cyclic conjugation in circumcoronenes is analyzed by means of its energy-effect, and found to agree with the predictions of Clar's aromatic sextet theory only in the case of B1 and B2.

The evaluation of spectral moments for molecular graphs of phenylenes

1997 ◽  
Vol 96 (4) ◽  
pp. 256-260 ◽  
Author(s):  
Svetlana Marković ◽  
Aleksandra Stajković
Keyword(s):  
Spectral Moments ◽  
Molecular Graphs

Bond Phase Determination of HOMO/LUMO and ‘Ethylene’ in Benzenoid Hydrocarbons

2002 ◽  
Vol 57 (11) ◽  
pp. 854-856
Author(s):  
Tetsuo Morikawa ◽  
Susumu Narita ◽  
Tai-ichi Shibuyaa
Keyword(s):  
Molecular Orbital ◽  
Molecular Orbital Theory ◽  
Orbital Theory ◽  
Benzenoid Hydrocarbons ◽  
Phase Determination ◽  
Molecular Graphs ◽  
Homo And Lumo ◽  
Valence Theory ◽  
Homo Lumo

Classical valence theory suggests the existence of strongly localized bonds (double bonds), i.e., of ethylene-like molecules, in benzenoid hydrocarbons (molecular graphs Bs); such an ‘ethylene’ is an edge in a hexagon that contacts with three hexagon faces in B. The phase of a bond is defined as the sign either plus for bonding or minus for antibonding. By use of perturbation molecular orbital theory we conclude that the phase of each bond that meets at the ethylene has necessarily the minus sign in HOMOof B; the bond phase alters in HOMO and LUMO of B.

scholarly journals On a class of approximate formulas for total ח-electron energy of benzenoid hydrocarbons

2001 ◽  
Vol 66 (2) ◽  
pp. 101-106 ◽  
Author(s):  
Ivan Gutman ◽  
Tanja Soldatovic
Keyword(s):  
Electron Energy ◽  
Benzenoid Hydrocarbons ◽  
Spectral Moments ◽  
Total Electron ◽  
Total Electron Energy ◽  
Approximate Formulas

The method for obtaining approximate formulas of the (n, m)-type for the total -electron energy of benzenoid hydrocarbons (communicated in J. Serb. Chem. Soc. 54 (1989) 189) is simplified and extended so as to include arbitrary spectral moments. The accuracy of the formulas thus obtained is very good and these need no additional fitting by means of empirically determined parameters.

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